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The Shapley value is the prevalent solution for fair division problems in which a payout is to be divided among multiple agents. By adopting a game-theoretic view, the idea of fair division and the Shapley value can also be used in machine…

Computer Science and Game Theory · Computer Science 2026-05-13 Guilherme Dean Pelegrina , Patrick Kolpaczki , Eyke Hüllermeier

Coalition formation explores how to partition a set of $n$ agents into disjoint coalitions according to their preferences. We consider a cardinal utility model with an additively separable aggregation of preferences and study the online…

Computer Science and Game Theory · Computer Science 2025-03-11 Martin Bullinger , René Romen

We consider transferable-utility profit-sharing games that arise from settings in which agents need to jointly choose one of several alternatives, and may use transfers to redistribute the welfare generated by the chosen alternative. One…

Theoretical Economics · Economics 2019-09-26 Moshe Babaioff , Uriel Feige

In Network games under cooperative framework, the position value is a link based allocation rule. It is obtained from the Shapley value of an associated cooperative game where the links of the network are considered players. The Shapley…

Theoretical Economics · Economics 2023-08-08 Niharika Kakoty , Surajit Borkotokey , Rajnish Kumar , Abhijit Bora

An increasing number of businesses and organisations rely on existing users for finding new users or spreading a message. One of the widely used "refer-a-friend" mechanisms offers an equal reward to both the referrer and the invitee. This…

Computer Science and Game Theory · Computer Science 2014-04-03 Talal Rahwan , Victor Naroditskiy , Tomasz Michalak , Michael Wooldridge , Nicholas R Jennings

In cooperative games with transferable utilities, the Shapley value is an extreme case of marginalism while the Equal Division rule is an extreme case of egalitarianism. The Shapley value does not assign anything to the non-productive…

Theoretical Economics · Economics 2022-01-25 D. Choudhury , S. Borkotokey , Rajnish Kumar , Sudipta Sarangi

The airport game is a classical and well-known model of fair cost-sharing for a single facility among multiple agents. This paper extends it to the so-called assignment setting, that is, for multiple facilities and agents, each agent…

Computer Science and Game Theory · Computer Science 2021-05-06 Yuki Amano , Ayumi Igarashi , Yasushi Kawase , Kazuhisa Makino , Hirotaka Ono

In networked communications nodes choose among available actions and benefit from exchanging information through edges, while continuous technological progress fosters system functionings that increasingly often rely on cooperation. Growing…

Computer Science and Game Theory · Computer Science 2018-09-10 Giovanni Rossi

The Shapley value (SV) and Least core (LC) are classic methods in cooperative game theory for cost/profit sharing problems. Both methods have recently been proposed as a principled solution for data valuation tasks, i.e., quantifying the…

Machine Learning · Computer Science 2022-04-08 Tianhao Wang , Yu Yang , Ruoxi Jia

Data valuation is an essential task in a data marketplace. It aims at fairly compensating data owners for their contribution. There is increasing recognition in the machine learning community that the Shapley value -- a foundational…

Cryptography and Security · Computer Science 2023-02-20 Zhihua Tian , Jian Liu , Jingyu Li , Xinle Cao , Ruoxi Jia , Jun Kong , Mengdi Liu , Kui Ren

This paper re-examines the Shapley value methods for attribution analysis in the area of online advertising. As a credit allocation solution in cooperative game theory, Shapley value method directly quantifies the contribution of online…

Econometrics · Economics 2018-04-17 Kaifeng Zhao , Seyed Hanif Mahboobi , Saeed R. Bagheri

Network-based systems are inherently interconnected, with the design and performance of subnetworks being interdependent. However, the decisions of self-interested operators may lead to suboptimal outcomes for users and the overall system.…

Systems and Control · Electrical Eng. & Systems 2026-02-11 Mingjia He , Andrea Censi , Runyu Zhang , Emilio Frazzoli , Gioele Zardini

Cooperative game theory has become a cornerstone of post-hoc interpretability in machine learning, largely through the use of Shapley values. Yet, despite their widespread adoption, Shapley-based methods often rest on axiomatic…

Machine Learning · Statistics 2025-06-18 Marouane Il Idrissi , Agathe Fernandes Machado , Arthur Charpentier

This paper addresses the benefit allocation in a mixed-energy truck platoon composed of fuel-powered and electric trucks. The interactions among trucks during platoon formation are modeled as a coalitional game with transferable utility. We…

Systems and Control · Electrical Eng. & Systems 2025-07-24 Ting Bai , Karl Henrik Johansson , Jonas Mårtensson , Andreas A. Malikopoulos

We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to…

Computer Science and Game Theory · Computer Science 2017-11-28 Matthias Feldotto , Martin Gairing , Grammateia Kotsialou , Alexander Skopalik

This paper investigates the impact of mechanism design on collaborative learning systems enabled by federated learning (FL). We propose a multi-action collaborative federated learning (MCFL) framework, capturing the interplay between agent…

Computer Science and Game Theory · Computer Science 2026-03-24 Meng Qi , Mingxi Zhu

The purpose of this study is to propose a model that predicts the social and psychological factors that affect the individuals collaborative learning outcome in group projects. The model is established on the basis of two theories, namely,…

Computers and Society · Computer Science 2016-10-18 Sara Taraman , Yasmin Hassan , Doaa Shawky , Ashraf H. Badawi

"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining…

Machine Learning · Computer Science 2023-03-07 Ruoxi Jia , David Dao , Boxin Wang , Frances Ann Hubis , Nick Hynes , Nezihe Merve Gurel , Bo Li , Ce Zhang , Dawn Song , Costas Spanos

In collaborative learning with streaming data, nodes (e.g., organizations) jointly and continuously learn a machine learning (ML) model by sharing the latest model updates computed from their latest streaming data. For the more resourceful…

Machine Learning · Computer Science 2023-06-12 Xiaoqiang Lin , Xinyi Xu , See-Kiong Ng , Chuan-Sheng Foo , Bryan Kian Hsiang Low

We consider game-theoretically secure distributed protocols for coalition games that approximate the Shapley value with small multiplicative error. Since all known existing approximation algorithms for the Shapley value are randomized, it…

Computer Science and Game Theory · Computer Science 2024-12-30 T-H. Hubert Chan , Qipeng Kuang , Quan Xue